You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Laws of the Iterated Logarithm for the Empirical Characteristic Function
Michael T. Lacey
The Annals of Probability
Vol. 17, No. 1 (Jan., 1989), pp. 292-300
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2244211
Page Count: 9
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Let X be a real-valued random variable with distribution function F(x) and characteristic function c(t). Let Fn(x) be the nth empirical distribution function associated with X and let cn(t) be the characteristic function Fn(x). Necessary and sufficient conditions in terms of c(t) are obtained for cn(t) - c(t) to obey bounded and compact laws of the iterated logarithm in the Banach space of continuous complex-valued functions on [ -1, 1 ].
The Annals of Probability © 1989 Institute of Mathematical Statistics